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12.Kinetic Theory of Gases
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A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly broght to rest. Assuming no heat is lost to the surroundings, its temperature increases by
A
$\frac{{\gamma M{v^2}}}{{2R}}K$
B
$\frac{{\left( {\gamma - 1} \right)}}{{2R}}M{v^2}K$
C
$\frac{{\left( {\gamma - 1} \right)}}{{2\left( {\gamma + 1} \right)R}}M{v^2}K$
D
$\frac{{\left( {\gamma - 1} \right)}}{{2\gamma R}}M{v^2}K$
Solution
$\frac{1}{2} \mathrm{mv}^{2}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}$
$\frac{1}{2} \mathrm{mv}^{2}=\frac{\mathrm{m}}{\mathrm{M}}\left(\frac{\mathrm{R}}{\gamma-1}\right) \Delta \mathrm{T}$
$\Delta \mathrm{T}=\frac{(\gamma-1) \mathrm{Mv}^{2}}{2 \mathrm{k}}$
Standard 11
Physics
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